B-spline estimation for partially linear varying coefficient composite quantile regression models

Abstract

In this article, a new composite quantile regression estimation (CQR) approach is proposed for partially linear varying coefficient models (PLVCM) under composite quantile loss function with B-spline approximations. The major advantage of the proposed procedures over the existing ones is easy to implement using existing software, and it requires no specification of the error distributions. Under the regularity conditions, the consistency and asymptotic normality of the estimators are also derived. Finally, a simulation study and a real data application are undertaken to assess the finite sample performance of the proposed estimation procedure.

Keywords:

• Partially linear varying coefficient
• composite quantile regression
• B-spline

Acknowledgments

This research was supported by the National Natural Science Foundation of China (11471264) and (11361015). The authors thank Drs Huang and Wu for allowing us to use the dataset” MACS Public Use Data Set Release PO4 ($1984\sim 1991$)”.